ASA 126th Meeting Denver 1993 October 4-8

2pPA4. A new explanation for the double resonance of a pure vapor bubble.

Yi Mao

Dept. of Phys. and Astron., Univ. of Mississippi, University, MS 38677

Lawrence A. Crum Ronald A. Roy

Univ. of Washington, Seattle, WA 98105

The second resonance frequency f[sub 0][sup (2)] of a pure bubble appeared first in R. D. Finch and E. A. Nippiras' theoretical analysis [J. Acoust. Soc. Am. 53, 1402--1410 (1973)]. However, no one has been able to observe a vapor bubble oscillating at f[sub 0][sup (2)]. A new analysis based on numerical calculations shows that f[sub 0][sup (2)] is physically unstable. By analogizing bubble oscillations with those of a mass-spring system, it is found that the resonance frequency F(f[sub d]) depends on the driving frequency f[sub d] and the real bubble resonance f[sub 0][sup (2)] is a solution of F(f[sub d])=f[sub d]. The behavior of F(f[sub d]) near f[sub d]=f[sub 0][sup (2)] shows that the bubble tends to shift its oscillation frequency away from f[sub 0][sup (2)] (repulsive); whereas F(f[sub d]) near the ordinary resonance f[sub 0][sup (1)] is attractive. A theory developed by the authors for directly calculating the resonance frequency and the damping constant without using the mass-spring analogy gives only f[sub 0][sup (1)]. Therefore, we are forced to the conclusion that f[sub 0][sup (2)] results from an improper mass-spring analogy and is not physically observable. [Work supported by ONR.]